cp's OEIS Frontend

Number of n-move sequences on a 3 X 3 X 3 Rubik's Cube (quarter-twists and half-twists count as moves, cf. A060010) that leave the cube unchanged, i.e. closed walks of length n from a fixed vertex on the Cayley graph of the cube with {F, F^(-1), F^2, R, R^(-1), R^2, B, B^(-1), B^2, L, L^(-1), L^2, U, U^(-1), U^2, D, D^(-1), D^2} as the set of generators. Alternatively, the n-th term is equal to the sum of the n-th powers of the eigenvalues of this Cayley graph divided by the order of the Rubik's cube group, ~4.3*10^19 (see A054434).